Dynamics of the Light-Cone Zero Modes: Theta Vacuum of the Massive Schwinger Model

The massive Schwinger model is quantized on the light cone with great care on the bosonic zero modes by putting the system in a finite (light-cone) spatial box. The zero mode of $A_{-}$ survives Dirac's procedure for the constrained system as a dynamical degree of freedom. After regularization and quantization, we show that the physical space condition is consistently imposed and relates the fermion Fock states to the zero mode of the gauge field. The vacuum is obtained by solving a Schr\"odinger equation in a periodic potential, so that the theta is understood as the Bloch momentum. We also construct a one-meson state in the fermion-antifermion sector and obtained the Schr\"odinger equation for it.Comment: 23 pages, RevTex, no figure

Differential membrane binding of α/β-peptide foldamers: implications for cellular delivery and mitochondrial targeting

The intrinsic pathway of apoptosis is regulated by the Bcl-2 family of proteins. Inhibition of the anti-apoptotic members represents a strategy to induce apoptotic cell death in cancer cells. We have measured the membrane binding properties of a series of peptides, including modified α/β-peptides, designed to exhibit enhanced membrane permeability to allow cell entry and improved access for engagement of Bcl-2 family members. The peptide cargo is based on the pro-apoptotic protein Bim, which interacts with all anti-apoptotic proteins to initiate apoptosis. The α/β-peptides contained cyclic β-amino acid residues designed to increase their stability and membrane-permeability. Dual polarisation interferometry was used to study the binding of each peptide to two different model membrane systems designed to mimic either the plasma membrane or the outer mitochondrial membrane. The impact of each peptide on the model membrane structure was also investigated, and the results demonstrated that the modified peptides had increased affinity for the mitochondrial membrane and significantly altered the structure of the bilayer. The results also showed that the presence of an RRR motif significantly enhanced the ability of the peptides to bind to and insert into the mitochondrial membrane mimic, and provide insights into the role of selective membrane targeting of peptides

Electromagnetic duality and light-front coordinates

We review the light-front Hamiltonian approach for the Abelian gauge theory in 3+1 dimensions, and then study electromagnetic duality in this framework.Comment: 18 pages, LaTeX, 2 references and a typo in an eqn. (19) corrected, minor revisions in response to referee's repor

Bubble Shape Oscillations and the Onset of Sonoluminescence

An air bubble trapped in water by an oscillating acoustic field undergoes either radial or nonspherical pulsations depending on the strength of the forcing pressure. Two different instability mechanisms (the Rayleigh--Taylor instability and parametric instability) cause deviations from sphericity. Distinguishing these mechanisms allows explanation of many features of recent experiments on sonoluminescence, and suggests methods for finding sonoluminescence in different parameter regimes.Comment: Phys. Rev. Lett., in pres

The (1+1)-dimensional Massive sine-Gordon Field Theory and the Gaussian Wave-functional Approach

The ground, one- and two-particle states of the (1+1)-dimensional massive sine-Gordon field theory are investigated within the framework of the Gaussian wave-functional approach. We demonstrate that for a certain region of the model-parameter space, the vacuum of the field system is asymmetrical. Furthermore, it is shown that two-particle bound state can exist upon the asymmetric vacuum for a part of the aforementioned region. Besides, for the bosonic equivalent to the massive Schwinger model, the masses of the one boson and two-boson bound states agree with the recent second-order results of a fermion-mass perturbation calculation when the fermion mass is small.Comment: Latex, 11 pages, 8 figures (EPS files

Mesons in the massive Schwinger model on the light-cone

We investigate mesons in the bosonized massive Schwinger model in the light-front Tamm-Dancoff approximation in the strong coupling region. We confirm that the three-meson bound state has a few percent fermion six-body component in the strong coupling region when expressed in terms of fermion variables, consistent with our previous calculations. We also discuss some qualitative features of the three-meson bound state based on the information about the wave function.Comment: 19 pages, RevTex, included 6 figures which are compressed and uuencode

Zero Mode and Symmetry Breaking on the Light Front

We study the zero mode and the spontaneous symmetry breaking on the light front (LF). We use the discretized light-cone quantization (DLCQ) of Maskawa-Yamawaki to treat the zero mode in a clean separation from all other modes. It is then shown that the Nambu-Goldstone (NG) phase can be realized on the trivial LF vacuum only when an explicit symmetry-breaking mass of the NG boson $m_{\pi}$ is introduced. The NG-boson zero mode integrated over the LF must exhibit singular behavior $\sim 1/m_{\pi}^2$ in the symmetric limit $m_{\pi}\to 0$, which implies that current conservation is violated at zero mode, or equivalently the LF charge is not conserved even in the symmetric limit. We demonstrate this peculiarity in a concrete model, the linear sigma model, where the role of zero-mode constraint is clarified. We further compare our result with the continuum theory. It is shown that in the continuum theory it is difficult to remove the zero mode which is not a single mode with measure zero but the accumulating point causing uncontrollable infrared singularity. A possible way out within the continuum theory is also suggested based on the ``$\nu$ theory''. We finally discuss another problem of the zero mode in the continuum theory, i.e., no-go theorem of Nakanishi-Yamawaki on the non-existence of LF quantum field theory within the framework of Wightman axioms, which remains to be a challenge for DLCQ, ``$\nu$ theory'' or any other framework of LF theory.Comment: 60 pages, the final section has been expanded. A few minor corrections; version to be published in Phys. Rev.

The Role of Zero-Modes in the Canonical Quantization of Heavy-Fermion QED in Light-Cone Coordinates

Four-dimensional heavy-fermion QED is studied in light-cone coordinates with (anti-)periodic field boundary conditions. We carry out a consistent light-cone canonical quantization of this model using the Dirac algorithm for a system with first- and second-class constraints. To examine the role of the zero modes, we consider the quantization procedure in {the }zero-mode {and the non-zero-mode} sectors separately. In both sectors we obtain the physical variables and their canonical commutation relations. The physical Hamiltonian is constructed via a step-by-step exclusion of the unphysical degrees of freedom. An example using this Hamiltonian in which the zero modes play a role is the verification of the correct Coulomb potential between two heavy fermions.Comment: 22 pages, CWRUTH-93-5 (Latex

Variational Mass Perturbation Theory for Light-Front Bound-State Equations

We investigate the mesonic light-front bound-state equations of the 't Hooft and Schwinger model in the two-particle, i.e. valence sector, for small fermion mass. We perform a high precision determination of the mass and light-cone wave function of the lowest lying meson by combining fermion mass perturbation theory with a variational approach. All calculations are done entirely in the fermionic representation without using any bosonization scheme. In a step-by-step procedure we enlarge the space of variational parameters. For the first two steps, the results are obtained analytically. Beyond that we use computer algebraic and numerical methods. We achieve good convergence so that the calculation of the meson mass squared can be extended to third order in the fermion mass. Within the numerical treatment we include higher Fock states up to six particles. Our results are consistent with all previous numerical investigations, in particular lattice calculations. For the massive Schwinger model, we find a small discrepancy (less than 2 percent) in comparison with known bosonization results. Possible resolutions of this discrepancy are discussed.Comment: some points clarified, representation straightened, to appear in Phys. Rev. D, 31 pages, Latex, REVTeX, epsfig, 3 postscript figures include

Nonperturbative Light-Front QCD

In this work the determination of low-energy bound states in Quantum Chromodynamics is recast so that it is linked to a weak-coupling problem. This allows one to approach the solution with the same techniques which solve Quantum Electrodynamics: namely, a combination of weak-coupling diagrams and many-body quantum mechanics. The key to eliminating necessarily nonperturbative effects is the use of a bare Hamiltonian in which quarks and gluons have nonzero constituent masses rather than the zero masses of the current picture. The use of constituent masses cuts off the growth of the running coupling constant and makes it possible that the running coupling never leaves the perturbative domain. For stabilization purposes an artificial potential is added to the Hamiltonian, but with a coefficient that vanishes at the physical value of the coupling constant. The weak-coupling approach potentially reconciles the simplicity of the Constituent Quark Model with the complexities of Quantum Chromodynamics. The penalty for achieving this perturbative picture is the necessity of formulating the dynamics of QCD in light-front coordinates and of dealing with the complexities of renormalization which such a formulation entails. We describe the renormalization process first using a qualitative phase space cell analysis, and we then set up a precise similarity renormalization scheme with cutoffs on constituent momenta and exhibit calculations to second order. We outline further computations that remain to be carried out. There is an initial nonperturbative but nonrelativistic calculation of the hadronic masses that determines the artificial potential, with binding energies required to be fourth order in the coupling as in QED. Next there is a calculation of the leading radiative corrections to these masses, which requires our renormalization program. Then the real struggle of finding the right extensions to perturbation theory to study the strong-coupling behavior of bound states can begin.Comment: 56 pages (REVTEX), Report OSU-NT-94-28. (figures not included, available via anaonymous ftp from pacific.mps.ohio-state.edu in subdirectory pub/infolight/qcd